Wash. Rev. Code § 53.46.080
If the district includes area from two or more counties, it shall be the duty of the county assessor in each county to certify annually to the auditor of his or her county, who shall forward the same to the principal county auditor, the total assessed valuation of that part of the port district which lies within his or her county. The port commission of such consolidated port district shall certify to the principal county auditor the budget and the levies to be assessed for port purposes: PROVIDED, That the amount of tax to be levied upon taxable property of that part of a port district lying in one county shall be in such ratio to the whole amount levied upon the property lying in the entire consolidated port district as the assessed valuation lying in such county bears to the assessed valuation of the property in the entire consolidated port district.
Thereafter the principal county auditor shall forward a certificate to each county auditor, for the county commissioners thereof, which shall specify the proportion of taxes to be levied for port district purposes.
RCW 53.46.080